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Large bending strains in an orthotropic beam with a preliminarily stretched or compressed layer: Exact solution

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Abstract

The model of an orthotropic nonlinear elastic compressible material generalizing the known model of an isotropic semilinear (harmonic) material and admitting a number of exact solutions at large strains is proposed. For this model of the material, an exact solution of the plane problem on large bending strains of a compound rectangular beam consisting of two layers, one of which is preliminarily deformed, is obtained. When formulating and solving the problem, the theory of superimposed large strains is used. On the basis of the calculations carried out, the effect of anisotropy on a strong bending of the compound beam with a preliminarily deformed layer is analyzed.

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References

  1. A. I. Lur’e, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

  2. V. A. Levin, Intern. J. Solids and Struct. 35, 2585 (1998).

    Article  Google Scholar 

  3. V. A. Levin, Repeated Superposition of Large Strains in Elastic and Viscoelastic Solids (Nauka, Moscow, 1999) [in Russian].

    Google Scholar 

  4. S. G. Lekhnitskii, Theory of Elasticity of Anisotropic Solid (Nauka, Moscow, 1977) [in Russian].

    MATH  Google Scholar 

  5. L. M. Zubov, Izv. Sev.-Kavkaz. Nauch. Tsentra Vyssh. Shk. Estestv. Nauki, No. 2, 27 (1976).

    Google Scholar 

  6. V. A. Levin, L. M. Zubov, and K. M. Zingerman, Dokl. Phys. 60 (1), 24 (2015).

    Article  ADS  Google Scholar 

  7. V. A. Levin, L. M. Zubov, and K. M. Zingerman, Dokl. Akad. Nauk 461 (4), 410–413 (2015).

    MathSciNet  Google Scholar 

  8. V. A. Levin, L. M. Zubov, and K. M. Zingerman, Intern. J. Solids and Struct. 67/68, 244 (2015).

    Article  Google Scholar 

  9. A. A. Zelenina and L. M. Zubov, Prikl. Mat. Mekh. 64 (3), 416 (2000).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, 119991, Russia

    V. A. Levin

  2. Southern Federal University, Rostov-on-Don, 344090, Russia

    L. M. Zubov

  3. Tver State University, Tver, 170100, Russia

    K. M. Zingerman

  4. OOO “Fidesis”, Moscow, Russia

    K. M. Zingerman

Authors
  1. V. A. Levin
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  2. L. M. Zubov
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  3. K. M. Zingerman
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Corresponding author

Correspondence to V. A. Levin.

Additional information

Original Russian Text © V.A. Levin, L.M. Zubov, K.M. Zingerman, 2016, published in Doklady Akademii Nauk, 2016, Vol. 469, No. 6, pp. 676–679.

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Levin, V.A., Zubov, L.M. & Zingerman, K.M. Large bending strains in an orthotropic beam with a preliminarily stretched or compressed layer: Exact solution. Dokl. Phys. 61, 407–411 (2016). https://doi.org/10.1134/S1028335816080127

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  • DOI: https://doi.org/10.1134/S1028335816080127

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